Re: 微積分證明題
※ 引述《coffee1205 (佐岸)》之銘言：
: Let f(x)=x/|x|.Prove that limitf(x) does not exist?
: x->0
: Hint:Show that no number L qualifies as the limit because
: there always some x such that |x| < delta,but |f(x)-L|大於等於1/2
: ,no matter how small delta is taken.
: 這題我想很久,但是解不出來,有沒有哪位好心人士可以幫幫我,小弟感激不盡!!!
我解出來是這樣的,不知道對不對?
For all eplison > 0, there exist delta > 0, such that |f(x)-L| < eplison
if 0 < |x-0| < delta
Assume the limit exist,take eplison=1/2
|f(x)-L|=|x/|x| - L|
=1+|L| 大於等於 1 > 1/2 = eplison
thus it is contridiction,so the limit does not exist.
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